Non-collinear equilibrium points in the perturbed restricted three-body problem with unstable elongated primary

IF 1.6 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY
Ravi Kumar Verma, Badam Singh Kushvah
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Abstract

In this paper, we have studied the motion around the non-collinear equilibrium points in the perturbed circular restricted three-body problem. The bigger primary is considered a point mass, and the smaller primary is an unstable elongated primary. The unstable elongated primary refers to the elongated primary rotates about its centre point, i.e. at an instant, the line joining the two ends of the elongated primary and the x-axis makes an angle, \(\theta \in [0,360^\circ )\). Computations of the non-collinear equilibrium points \(L_{4,5}\), and their linear stability, are investigated, and the results are applied to the Jupiter-Amalthea, Saturn-Prometheus and Pluto-Hydra systems. It is found that the positions of the non-collinear equilibrium points \(L_{4,5}\) remain unchanged with variation in the angle, \(\theta \), but small variation in the critical mass parameter, \(\mu _c\) is observed. Variations of the critical mass, \(\mu _c\), with different segment-length and its rotation are studied. Stable solutions around \(L_4\) are obtained in the systems of Jupiter-Amalthea, Saturn-Prometheus, and Pluto-Hydra using the established results.

Abstract Image

具有不稳定拉长原基的扰动受限三体问题中的非共轭平衡点
在本文中,我们研究了扰动圆形受限三体问题中围绕非共线平衡点的运动。较大的原基被认为是一个点质量,较小的原基是一个不稳定的拉长原基。不稳定拉长原基是指拉长原基围绕其中心点旋转,即在某一时刻,拉长原基两端与 x 轴的连线成一个角度,(theta \in [0,360^\circ )\).研究了非共线平衡点 \(L_{4,5}\)的计算及其线性稳定性,并将结果应用于木星-马耳忒斯、土星-普罗米修斯和冥王星-海德拉系统。研究发现,非共线平衡点 \(L_{4,5}\)的位置随角度 \(\theta \)的变化而保持不变,但临界质量参数 \(\mu _c\)的变化较小。研究了临界质量(\(\mu _c\))随不同段长及其旋转的变化。在木星-马耳忒亚星系、土星-普罗米修斯星系和冥王星-海德拉星系中,利用既定结果得到了 \(L_4\) 附近的稳定解。
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来源期刊
Indian Journal of Physics
Indian Journal of Physics 物理-物理:综合
CiteScore
3.40
自引率
10.00%
发文量
275
审稿时长
3-8 weeks
期刊介绍: Indian Journal of Physics is a monthly research journal in English published by the Indian Association for the Cultivation of Sciences in collaboration with the Indian Physical Society. The journal publishes refereed papers covering current research in Physics in the following category: Astrophysics, Atmospheric and Space physics; Atomic & Molecular Physics; Biophysics; Condensed Matter & Materials Physics; General & Interdisciplinary Physics; Nonlinear dynamics & Complex Systems; Nuclear Physics; Optics and Spectroscopy; Particle Physics; Plasma Physics; Relativity & Cosmology; Statistical Physics.
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